Using error bounds to compare aggregated generalized transportation models

Abstract

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude that calculating the a priori error bound can be considered as a useful strategy to select the appropriate aggregation level. The a posteriori error bound provides a good quantitative measure of the actual error.

The Planning of Guaranteed Targeted Display Advertising

“…Much of what we do focuses on restoring feasibility; thus, our work contributes to the aggregation literature for the special case of quadratic transportation problems that arise in GTDA planning. We should note that in addition to Zipkin (1980a), aggregation has been studied in the context of generalized transportation networks (Litvinchev and Rangel 2006), linear programs (Zipkin 1980b, Zipkin 1980c, and Leisten 1997, stochastic programs (Birge 1985, Wright 1994, and convex network programs (Zipkin 1982). The surveys by Rogers et al (1991) and Vakhutinsky et al (1979) list the bounds known at that time, and the book by Litvinchev and Tsurkov (2003) is also a good reference.…”